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THE 



ABC 



OF 



Life Insurance. 



By CHARLES E. WILLARD. 




PUBLISHED BY 

THE SPECTATOR COMPANY, 

New York and Chicago. 
1889. 



.wc? 



Entered in the office of the Librarian of Congress, at Washington, D. C, in 
the year 1888, by The Spectator Company, New York. 



PREFACE. 

To explain and illustrate some of the fundamental and 
elementary principles of Life Insurance so simply that they 
can readily be understood by men who have not been 
specially trained as mathematicians, or have not had their 
attention particularly directed to the theory and mathe- 
matics of Life Insurance, is the aim of this little book. 
For those who already possess this elementary knowledge, 
there are many excellent hand-books which carry the dis- 
cussion much further, and cover the entire subject in the 
ablest and most satisfactory manner. But as an intro- 
duction to these, a beginning, an "easy lesson," it is 
hoped that the following pages will have their use. They 
owe their existence to the impossibility of finding among 
the text-books already published, anything which seemed 
exactly adapted to this purpose. C. E. W. 

New York, November i, 1888. 



THE 



ABC 

OF 

LIFE INSURANCE 



CHAPTER I. 

A PRELIMINARY STUDY, 

Insurance, in its simplest form, is indemnity for loss. 
Or it may be described as a method of distributing an 
individual's loss among a large number of other persons 
who are willing to assume each his small share of it, in 
return for the certainty that if a similar loss falls upon any 
one of them, the loser, or those dependent upon him, will 
in like manner be indemnified. If a building or stock of 
goods is burned, so much capital is destroyed. If a pro- 
ductive human life ends, so much capital in another form is 
destroyed. For convenience in apportioning the loss, or 
dividing it among those interested, the machinery and organ- 
ization of a company are invoked. The company contracts 
to pay the loss, the company collects the premium, the 
company pays the loss if it occurs. Consequently, the com- 

NOTE. — It is sometimes flippantly said that insurance is simply a form 
of gambling, the company betting a large sum that a certain loss will not 
occur, the insured betting a small sum that it will ; if the loss occurs, the 
company pays the bet. In so foolish a statement as this, only the element 
of chmce is taken into account. No consideration is had of the fact that 
the insured receives the worth of his money, in any event, in the protec- 
tion afforded — the certainty that he will be indemnified if the loss falls on 
him. A bet involves the payment of money without any equivalent in 
return. 



6 The A B C of Life Insurance. 

pany is said to insure each individual, but it must be 
remembered that the actual function of the company is 
that of a medium through which the business is transacted, 
and that the result is simply the apportionment of such 
individual losses as occur, among a large number of insured 
who assume the payment of these losses from year to year 
in order that they may themselves claim a like indemnity 
should the occasion arise. If this fact were thoroughly 
understood in life insurance, as it is in fire, more correct 
ideas of the values of life policies would prevail even among 
those who have no technical knowledge of the subject. 

Two or three elementary principles constitute the foun- 
dation of all life insurance. They are so simple that they 
need only to be presented to be comprehended by any 
person of ordinary intelligence. Their practical application 
to various contingencies may, and often does, involve 
mathematical calculations which are not only very lengthy 
but also very intricate. This fact has thrown a veil of 
mystery over the whole subject, which does not properly 
belong to it. One need not be an actuary or expert 
mathematician to have a very fair knowledge of the funda- 
mental principles. The following example will enable us 
to study these principles : 

// should be understood in advance that the supposed con- 
ditions of this example, so far as the rate of mortality {or 
number of deaths in a year) is concerned, are not those 
which we meet in actual experience. The term of life is 
shortened from ninety -six years to fifty, that the calculation 
may be proportionately shortened. The number of deaths 
each year, and the amount of insurance o?i each individual, 
are purposely such as to make the calculation ve?y simple, 
and susceptible of instant verification. Consequently, our 



The A B C of Life Insurance. 7 

results will not be the results of actual experience. The 
premium will be very much too high, the annual cost of the 
insurance very ?nuch too great, the accumulation of reserve 
very much too rapid. 

But the two or three elementary principles which we wish 
to study are perfectly and exactly illustrated. As will be 
shown later on, the same process applied to the conditions 
which actually exist, will secure correct results. 

Bearing this in Mind : 

Let us suppose that a company is formed of i ooo men ; 
that the age of each man is 40 ; that each is insured for 
$1100; that 100 men will die during the first and each 
succeeding year ;* that every man remains in the company 
until his death occurs ; that the company receives nothing 
for interest on money in its hands, and pays nothing for the 
expense of conducting the business. Suppose, also, that 
for the sake of convenience these men agree to pay a uni- 
form amount each year so long as they live, as a premium 
for the insurance. 

It is evident that the total amount of insurance to be 
paid would be 1000 x $1100, or $1,100,000. 

It is also evident that there would be 1000 men to pay 
premiums the first year, 900 the second year, 800 the third 
year, and so on. The total number of premium payments 
made would be 5500. Each payment therefore must be 
$1,100,000 •+- 5500, or $200, which, upon our assumption, 

* As a matter of fact, we should expect that the number of deaths among 
1000 men, age 40, would be but 9 or 10 the first year, and that 1 or 2 cf 
the 1000 men would survive the age of 90. To make our supposition 
conform to these facts would extend our calculation over 50 years. The 
assumption which is made above, reduces the term to 10 years, and so 
avoids the tediousness of the calculation based upon the longer, actual 
term. 



8 The A B C of Life Insurance. 

would be the annual, whole-life premium for an insurance of 
$1100 upon the life of a man aged 40. 

The results would be as follows : 

i.ooo x $200 = $200,000, Premiums received beginning of First 

100 x $1,100-- 110,000, Losses paid during I, Year, 

Age 40. 



$90,000, Amount in hand at end of J 

900 x $200 = $180,000, Premiums received beginning of v 

$270,000, Total am't in hand beginning of 
100 x $i,ico = 110,000, Losses paid during 

$160,000, Amount in hand at end of 
800 x $200 == 160,000, Premiums received beginning of 1 



$320,000, Total am't in hand beginning of Th ^ rc * 

tt/~> /-k/-v\ T ^ccoc i-ioirl rlnrinrr I 



Second 

Year, 

Age 41. 



Age 42. 



Fourth 

Year, 

Age 43. 



100 x $1,100= 110,000, Losses paid during 

$210,000, Amount in hand at end of 

700 x $200= 140,000, Premiums received beginning of > 

$350,000, Total am't in hand beginning of 
100 x $1,100= 110,000, Losses paid during 

$240,000, Amount in hand at end of J 

600 x $200 == 120,000, Premiums received beginning of ^ 

$360,000, Total am't in hand beginning of K^^ 1 

100 x $1,100= 110,000, Losses paid during J ^ ^ 

$250,000, Amount in hand at end of J 

500 x $200= 100,000, Premiums received beginning of "| 

$350,000, Tot il am't in hand beginning of I Sixth 
100 x $1,100= 110,000, Losses paid during ^ ffe ' 

$240,000, Amount in hand at end of J 

^oo x $200 = 80,000, Premiums received beginning of ") 

$320,000, Total am't in hand beginning of I ^e ventn 



ico x $1,100= 110,000, Losses paid during 

$210,000, Amount in hand at end of 



Age 46. 



The A B C of Life Insurance. 

300 x $200 = 60,000, Premiums received beginning of 

$270,000, Total am't in hand beginning of 
100 x $1,100= iio.ooo, Losses paid during 



$160,000, Amount in hand at end of 

200 x $200 = 40,000, Premiums received beginn'ng of 

$200,000, Total am't in hand beginning of 
100 x $1,100= 110,000, Losses paid during 

$90,000, Amount in hand at end ot 

100 x $200= 20,000, Premiums received beginning of 



Eighth 

Year, 

Age 47. 



Ninth 

Year, 

Age 48. 




$no,oco, Total am't in hand beginning of 
$1,100= 110,000, Losses paid during 



Now it is evident that the principles involved in fixing 
the premium and collecting the necessary amounts to pay 
losses in full, until the last contract is met, must be the 
same, whether the death rate be 9 or 100 per annum, and 
the term 10 or 50 years. Let us see, then, what can be 
discovered by a study of the above. 

In the first place it is evident that the cost of the insur- 
ance — i. e., the amount of the losses in any one year 
divided by the number of men living at the beginning of 
that year — varies from year to year, although the annual 
premium remains the same. The losses for the first year 
are $110,000. The number of men to pay premiums 
is 1000. The cost of the insurance, therefore, is 
$110,000 -s- 1000, or $110 per man. The second year 
the losses are $110,000. There are but 900 men, how- 
ever, to pay premiums, 1 00 men having died. Conse- 
quently, the cost of the insurance is $110,000-^900, or 
$122.33 P er man - I n tne same way the cost the third 
year is $110,000.00-^-800, or $137.50 per man; the 
fourth year, $110, 000 +- 7 00, or $157.14 per man — and 
so on. When we reach a point where more than one-half 



io The A B C of Life Insurance, 

of the original number of men is dead, or will have died 
before the end of the year, the cost will exceed the premium. 
Thus, in the sixth year, the cost is $110,000 -*- 500, or 
$220.00 per man. And, from this point, the cost con- 
tinues to exceed the premium by an annually increasing 
amount to the end. 

It is evident, therefore, that a uniform or, as it is usually 
called, a " level " premium, involves the annual payment of 
a sum in excess of the current cost of the insurance during 
a part of the term, and the annual payment of a sum less 
than the current cost of the insurance during the remainder 
of the term. Consequently, whatever is overpaid during 
the former portion of the term must be held in hand, 
reserved, to provide against the deficit which would other- 
wise occur during the latter part of the term. 

The same fact appears from an inspection of the figures 
above, without stopping to calculate the cost of the insur- 
ance. Thus we see that the premiums received exceeded 
the losses paid by $90,000 the first year, $70,000 the 
second year, and so on up to the sixth year. Then the 
losses began to exceed the premiums, the excess being 
$70,000 in the ninth year, and $90,000 in the tenth year. 
If, now, the company finding itself with $90,000 in hand at 
the end of the first year, $160,000 at the end of the second 
year, $210,000 at the end of the third year, had overlooked 
the call to be made upon these funds in the future, and had 
spent or, through carelessness or misfortune, lost some of 
these funds, had failed to keep the full amount intact, there 
would have been finally a deficit of exactly the amount so 
lost or spent. Ten thousand dollars a year might be spent 
for several successive years without affecting the company's 
ability to pay its current losses, but the time would surely 
come when the absence of the money would show itself in 



The A B C of Life Insurance, 1 1 

the inability of the company to carry its contracts of insur- 
ance to the end. It is plain, therefore, that at the end of 
each year the company would have in its possession a sum 
of money which it must carefully reserve for the future 
fulfillment of its existing contracts. 

Another point. At the beginning of each year (for the 
above exampl- supposes that the company receives all its 
premiums at the beginning of the year), there would be on 
hand the money brought over from the preceding year plus 
the premiums for the current year. A portion of this 
total amount would have to be held for the payment of the 
current losses of this year. To distinguish this from the 
amount to be carried forward at the end of the year, we will 
call it the insurance reserve. Since this would be paid out 
at intervals during the year, as losses occurred, the sum left 
in the company's hands would slowly diminish until, at the 
end of the year, the insurance reserve would be entirely (and 
properly) expended in the payment of losses, and only that 
amount of money which must be held for the future would 
remain. This latter amount, since it must be held for a 
series of years, and might be invested in interest-bearing 
securities, we will call the investment reserve. 

This suggests another point, viz.: that while the reserve cf 
a policy may be said to increase each year that the insur- 
ance is in force, this increase, so long as premiums are paid, 
is not an absolutely uniform one. The reserve is greater at 
the beginning of the year, because it includes both the 
insurance and the investment portions ; diminishes during 
the year, because the insurance portion is expended grad- 
ually in the payment of losses ; but at the end of each year 
is greater than at the end of the preceding year, because the 
investment portion of that year is added to the investment 
portion of the preceding year or series of years. 



12 The A B C of Life Insurance. 

If we divide the amount of money in the hands of our 
supposed company at the end of the first year by the num- 
ber of survivors at the end of that year, we have $90,000 -f- 
900, or $100. This is the amount of reserve for each policy 
(or insurance) at the end of the first year. After the pre- 
miums have been paid at the beginning of the second year, 
and before any deaths have occurred for that year, the reserve 
on each policy would be $270,000 -s- 900, or $300. At the 
end of that year the reserve would be $160,000 -*- 800, or 
$200 on each insurance. By putting the figures of reserves 
at the beginning and end of several years in parallel col- 
umns, this point will be more clearly seen : 

Beginning End 

of Year. of Year. 

Reserve second year $300 $200 

Reserve third year 400 300 

Reserve fourth yeai 500 400 

Reserve fifth year 600 500 

This may be represented by a diagram as follows : 

Fifth Year. 



Second Year. 




Perhaps the function of the investment reserve may be 
shown in another way. Suppose that the company of 1000 



The A B C of Life Insurance. 13 

men had agreed to pay each year the exact cost of the 
insurance for that year. Taking our figures of cost on page 
8, the results would be as follows : 

1,000 x $110 =$110,000, Premiums rec'd beginning of 1 ~ . 
100 x $1,100 = 110,000, Losses paid during 1 Year, 

oo, Amount in hand at end of j 

900 x $122.23 = $110,000, Premiums rec'd beginning of ") Second 
100 x $1,100 = 110,000, Losses paid during I Year, 

00, Amount in hand at end of J 

800 x $137-50 = $110,000, Premiums rec'd beginning cf ^ 'rvxrA 
100 x $1,100 = 110,000, Losses paid during I Year, 

00, Amount in hand at end of J 

etc., etc., etc. 

Here, as the increasing premiums take care of the current 
losses for each year, there is no need of carrying any amount 
forward from one year to another, and the investment re- 
serve disappears altogether. The insurance reserve at the 
beginning of each year is the full amount of the expected 
losses for that year. As these losses occur and are paid the % 
reserve diminishes, and at any time during the year is 
measured by the amount of expected losses for the re- 
mainder of the year. At the end of the year, all losses 
having been paid, it is nothing. 

It appears then, that, leaving out the question of ex- 
penses, the level premium is made up of two parts — the 
insurance portion, which pays the current losses of the 
year, and the investment portion, whose sole purpose and 
use are to keep the premium level. The investment reserve 
(and this is what is usually meant by the term " Reserve ") 
may be defined as that part of a level or uniform premium, 
not needed for current losses, which is set aside for pur- 



14 The A B C of Life Insurance. 

poses of accumulation, to be used, with its accretions, in 
payment of future losses. 

Incidentally, it should be noted that the reserve of each 
policy in our example is $1100 at the tenth or final year, 
and that the actual cost of the insurance for that year is 
also $1100. 

From this preliminary study, then, it is evident that a 
company must either collect an annually increasing pre- 
mium, correctly adjusted to the annually increasing cost, or 
must accumulate from a level or uniform premium an invested 
reserve fund; that this reserve, if accumulated, must be 
kept intact until needed for its legitimate purpose, viz.: the 
payment of such a portion of each policy as that policy has 
contributed to it; that the waste or loss of this reserve 
means ultimate bankruptcy, on account of the increasing 
cost of the insurance for which the level premium, without 
the accumulated reserve, does not provide ; and that the 
reserve upon any policy increases with the age of that 
policy or the number of years it has been in force. We can 
also see that the man who wishes insurance must continue 

Note. — Another definition of a reserve is " The difference between 
the present value of the insurance, and the present value of the future 
premiums on that insurance." As an illustration cf this definition, our 
example is very crude, since it ignores the question of compound interest, 
which is the important factor in determining present values. Neverthe- 
less, it suggests the method of calculating the reserves for insurances at 
different ages and under policies upon which premiums have been paid 
for different terms of years, as actually practiced. Thus, in our supposed 
company, at the end of the third year there were 700 survivors, upon each 
one of whom there was an insurance of $1100, or a total of $770,000. The 
total amount of premiums to be paid during the remainder of the term of 
years covered by the example was $560,000. Of course, if interest is to 
be ignored, there is no difference between present and future values. 
Consequently, the present values of the insurances and of the future 
premiums would be their full amounts. The difference, $210,000, is the 
amount of the reserve at the end of the third year given in our example. 



The A B C of Life Insurance. 15 

to pay his premiums thereon ; that the men who die during 
the earlier part of the term do not pay the company, in pre- 
miums, an amount equal to the amount of their insurance ; 
and that the men who live to the latter part or end of the 
whole-life term pay, in premiums, more than the amount 
of their insurance. 

Simple and elementary as is the preceding discussion, it 
will repay careful study by anyone unfamiliar with the 
theory of insurance. And when its points have been mas- 
tered thoroughly, the preparation will be ample for a 
ready understanding of what follows in this little volume. 

Our illustration was based upon the supposition that the 
1000 men were all of the same age ; that no other men came 
into the arrangement; that none of the original number 
dropped out by the way ; that in each year the number of 
deaths was exactly what it was expected to be when the 
company was formed; that nothing was realized for interest 
by the investment of funds on hand; and that there was no 
expense connected with the transaction of the business. In 
actual experience, men of all ages are insured in the same 
company; new members are continually coining in; old 
ones are dropping out ; new sets of reserves are taking the 
places of those which have been applied in the payment of 
losses or have been withdrawn ; the rate of mortality varies 
more or less from the tabular rate ; interest is received on 
investments; and expenses are incurred in various ways. 
An attempt will be. made in the following pages to discuss 
some of these matters briefly and simply, but to carry the 
discussion only so far as may be necessary to an intelligent 
comprehension of the subject in a somewhat general way. 



16 The A B C of Life Insurance. 



CHAPTER II. 

MORTALITY TABLES. 

If insurance is simply a method of distributing or appor- 
tioning individual losses among a large number of people 
who enter into the arrangement for mutual protection, the 
fact will at once suggest itself that each person should pay 
not only in proportion to the amount of his possible loss, 
but also in proportion to the likelihood that that loss will 
occur. Risks are classified for fire insurance according to 
the hazard of fire. In like manner, the life most likely to 
end should pay the highest premium. Aside from the 
special risk to which any individual life may, at any given 
time, be subjected by reason of sickness or accident, 
it is evident that the older a man grows the nearer he 
is to death. Consequently, in determining the amount of 
premiums which any individual should pay, it is evident 
that his age must be the prime factor. The first thing, 
then, to be determined is the effect of age upon the rate of 
mortality — in other words, how many deaths within a year 
may be expected among a given number of men of any given 
age. 

No business in the world has a more reliable basis upon 
which to make its calculations than that of life insurance. 
The rate of mortality among lives of different ages has 
been made a matter of study and record for more than 150 
years. The tabulated results are known as " Mortality 
Tables" or " Tables of Mortality." 



The A B C of Life Insurance, 17 

The first used as a basis for life insurance was the North- 
ampton Table. This was formed by Dr. Price from obser- 
vations on the mortality in the town of Northampton, Eng- 
land, from 1735 t0 1 7 So. This table is no longer used for 
valuations, and has never been used in this country. 

The Carlisle Table was formed by Mr. Milne from obser- 
vations in the town of Carlisle, England, from 1778 to 1787. 
It is still in use to a limited extent. 

The Actuaries' or Combined Experience Table, published 
in 1843, was compiled from the experience of seventeen 
English companies. It is still used very generally in Eng- 
land for the computation of premiums, and in this country 
as the legal standard for computing reserves with four per 
cent interest. 

The Farr Table, No. 3, was constructed by Dr. Farr from 
observations upon the mortality of the entire population of 
England, and was published in 1864. It is not now in use. 

The American Experience Table was formed from the 
experience of the Mutual Life of New York by Mr. Sheppard 
Homans, actuary of that company. It is in general use in 
this country for the computation of premiums, and as the 
legal standard for computing reserves with four and one- 
half per cent interest. 

The experience of thirty American companies was tabu- 
lated by Mr. L. W. Meech, and the results published in 
1 88 1. This table is generally known as the Meech Table. 
It is very valuable as a record of actual experience, but is 
not used in valuations. 

For present purposes it is necessary to give the Actuaries' 
and American Experience tables only. These will be found 
on pages 51, 52 and 53. 

From the latter table anyone who is interested to do so, 
and has the time to spare, can substitute the proper figures 



1 8 The A B C of Life Insurance, 

for those given in the preliminary example, and can calcu- 
late the necessary annual, whole-life premium for any age 
without allowance for interest or expenses. 

By dividing the number of deaths during any year by the 
number of persons living at the beginning of that year, we 
obtain the percentage of mortality as given in connection 
with these tables. 

From the mortality tables, also, by averaging the after-life 
time of the number of persons living at any given age, we 
obtain the table of the Expectation of Life given on page 50. 
This table is interesting, but not particularly useful. It is 
never employed in making calculations. The supposition 
that the annual premium to be paid by a person of any 
given age is the sum which, invested at four or four and a 
half per cent during the " expectation " of that person, 
would equal the amount insured ; or that the present value 
of an insurance, payable at death, can be ascertained by 
discounting the amount of the insurance at four or four and 
a half per cent for the number of years represented by the 
" expectation " of the insured, is wholly erroneous. 

So, too, the average age of a number of lives is not a 
reliable measure of the risk upon them all. Thus, the 
average age of 10 men aged 98, and 10 men aged 30, 
would be 64 years. Among these 20 men we should 
expect at least 10 deaths during the year, while among 20 
men aged 64 we should not expect more than one death. 



The A B C of Life Insurance, 19 



CHAPTER III. 
NET PREMIUMS. 

A net premium is one in the calculation of which due 
allowance has been made for the interest which a company 
may receive upon its investments, but with no allowance for 
the expenses of the business. 

Thus far we have, for the sake of simplicity, neglected the 
question of interest. But, since a company may realize con- 
siderable amounts in the way of interest upon judiciously 
invested funds, not needed for present use, it is plain that, 
in determining the premium which it is necessary to charge, 
due consideration of this source of income should be had. 
Obviously, the rate of premium will be reduced by the fact 
that interest receipts are to be added to the company's in- 
come. If too great a reduction is made, however, the pre- 
mium will not be sufficient. And, as life insurance contracts 
may cover a very long period, premiums must be based 
upon assumptions which are likely to be realized in actual ex- 
perience through an indefinite term of years. With this fact 
in view, 4 per cent has been taken as the probable rate of 
interest, in the calculation of premiums. 

The following explanation of the method of calculating a 
net annual premium for an insurance for the term of five 
years, presents only the very simplest form of such calcula- 
tions, the design being rather to illustrate principles and the 
method of their application, than to present or attempt to 
demonstrate intricate mathematical problems. 



20 The A B C of Life Insurance. 

What should be the net annual premium (level) for an in- 
surance of $1000, for the term of 5 years only, upon the life 
of a man aged 40, according to the American Experience 
Table with 4 per cent interest ? 

An annuity is the recurring annual payment of a uniform 
amount. Consequently the annual premium is an annuity 
paid by the insured to the company. Manifestly, there- 
fore, the proper method of ascertaining the required pre- 
mium is to ascertain the present value of the insurance, and 
then to determine the amount of an annuity whose present 
value is equal to the present value of the insurance. We 
will calculate the present value of an insurance for $1 and 
then find the corresponding annuity. The latter will be the 
annual premium for an insurance of $1, which must be 
multiplied by the number of dollars of any desired insurance 
to obtain the necessary premium therefor. 

In this, and in all similar calculations, the premium is 
considered payable at the beginning of the year, and the loss 
at the end of the year. 

Present value of (or, in other words, single premium for) 
an insurance of $1, for a term of 5 years, upon the life of 
a man aged 40. 

By the American Experience Table (page 51) it appears 
that, out of 78,106 person living at age 40, there will die 

In the 1 st year, 765 persons. 
In the 2d " 774 " 
In the 3d " 785 
In the 4th " 797 
In the 5th " 812 

An insurarice of $1, therefore, upon each person, would 
require the payment of $765.00 at the end of the first year, 
$774.00 at the end of the second year, and so on. From the 



The A B C of Life Insurance. 21 

table of present values of $1 (page 56) we find that the 
Present value at 4 per cent of $1 payable in 1 year 

is $0.961538. 
Present value at 4 per. cent of $1 payable in 2 years 

is $0.924556, etc. 
Therefore the present value of the above losses is as 
follows : 

Ofthe$ 7 65.oo, $765 x .961538 $735-58 

Ofthe 774.00, 774 x .924556 7I5- 60 

Of the 785.00, 785 x .888996 697.86 

Ofthe 797.00, 797 x .854804 681.28 

Of the 812. oo, 812 x .821927 667.40 

Total present value of losses $3,497.72 

If the 78,106 persons living at the beginning of the term 
were to divide this present value into 78,106 single pay- 
ments, to be made at once, the result would be $3,497.72 
-j- 78,106, or $0.04478, and this would be the present value 
of an insurance of $1, and consequently the single pre- 
mium which each man should pay in advance for such an 
insurance. 

But we wish to find an annual premium (or annuity) 
whose present value shall equal the above present value of 
the insurance. This will, of course, be an annuity for 5 
years contingent upon the lives of 78,106 persons, aged 40. 
We will first find the present value of such an annuity 
for $1. 

By the same table of mortality, we find that if each per- 
son living at the beginning of each year should pay $1, 
the company would receive 

At the beginning ofthe 1st year, $78,106.00. 

At the beginning of the 2d year, 77,341.00. 
[ At the beginning of the 3d year, 76,567.00. 

At the beginning ofthe 4th year, 75,782.00. 

At the beginning of the 5th year, 74.985.00. 



22 The A B C of Life Insura?ice. 

Of course, the present value of the first payment would 
be the entire amount of that payment, since it is made at 
once. The present value of the second payment would be 
the present value of that amount payable in i year ; of the 
third, the present value of that amount payable in 2 years ; 
and so on. Resorting again to the table of present values 
of $1, we have 

Present value of the $78,106.00 $78,106.00 

Present value of the 77,341.00 = $77,341 x .961538 74,36631 

Present value oi the 76,567.00 = 76,567 x .924556 70,790.48 

Present value of the 75,782.00 = 75,782 x 888(596 67,369.89 

Present value of (he 74,985.00= 74,985 x .854804, 64,097.48 

Total present value of all the payments $354,730.16 

This total depends upon the lives of 78,106 persons — the 
number living at the beginning of the first year. Conse- 
quently, the amount depending upon the life of any one per- 
son must be ^ 354 ' 73 °; T , or $4.54164. This, then, is the 
78,106 

present value of an annuity of $1 for 5 years, contingent 
upon the life of a person aged 40. This value is much 
larger than the value of the insurance, which is only 
$0.04478. Consequently the required annuity or annual 

A AlSK 

premium will be only — ' of $1, or $0.00986. This is 

454,104 

the net annual premium for an insurance of $1 for the 

term of 5 years on a life aged 40. The premium for an 

insurance of $1000 would be 1000 x $0.00986, or $9.86. 

It will be seen at once that, if the term of the insurance, 
instead of being limited to 5 years, had covered the entire 
term of life according to the American Experience Table, 
the result would have been the net annual, whole-life pre- 
mium. 



The A B C of Life Insurance. 



23 



The following example carries the premium, interest, re- 
serve and loss accounts through the five-year term, with the 
above premium and with the rate of mortality shown by 
the American Experience Table: 

78,106 x $9.86 = $770,125 16, Premiums ree'd beginning of "* 
30,805.01, 4 per cent interest 



765 



77,341 x 



$800,930.17, Total 
$1000 = 765,000.00, Death claims durirg 

s3S.93°- I 7» Reserve end of 
$9.86 = 762.582.26, Premiums ree'd beginning of 

$798,512.43, Total beginning of 
31,940.50, 4 per cent interest 



76,567 x 

785 x 

75,782 x 

797 x 
74,985 x 

8l2 X 



$830,452.93, Total 
774 x $1000 = 774,000.00, Death claims during 



,.86 = 



$56,452.93, Reserve end of 

754,950.62, Premiums ree'd beginning of ' 



811,403.55, Total beginning of 
32,456.14, 4 per cent interest 



$843,859.69, Total 
f>iooo = 785,000.00, Death claims during 

$58,859.69, Reserve end of 
$9 86 = 747,210.52, Premiums ree'd beginning of " 

$806,070.21, Total beginning of 
32,242.81, 4 per cent interest 



.,313. 02, Total 
$1000 == 797,coo.oo, Death claims during 

$41,313.02, Reserve end of 
$9.86 = 739,352.10, Premiums ree'd beginning of 

$780,665.12, Total beginning of 
31,226.60, 4 per cent interest 

$811,891.72, Total 
$1000 = 812,000.00, Death claims during 



First 

Year, 

Age 40. 



Second 

Year, 

Age 41. 



Third 

Year, 

Age 42. 



Fourth 

Year, 

Age 43. 



Fifih 

Year, 

Age 44. 



Excess of death claims, $108.28 

The excess of the death claims, $108.28, represents about 
one-seventh of a cent for each person living at the end of 



2 4 The A B C of Life Insurance. 

the fifth year. It is impossible to express the premium 
more exactly, in dollars and cents, than $9.86. A pre- 
mium of $9.87 would show an excess of receipts over death 
claims of about $4,207.52, or 5.6 cents for each person 
living at the end of the term. 

The foregoing illustration shows that a considerable 
amount of work is involved in determining the premium 
for the simplest form of insurance for one age only, and 
for so short a term as five years. It will be seen at once 
that the computation of premiums for every age and for 
long terms would be an exceedingly laborious process. 
And when different forms of insurance and contingencies 
involving more than one life are to be considered, the 
mathematical problem may be one of great intricacy and 
difficulty. Logarithms, the processes of algebra, and 
various devices, such as " Commutation Columns," for 
lightening the labor of computation, are employed by the 
actuaries or expert mathematicians who make the calcula- 
tions. One who desires to acquaint himself with the mathe- 
matics of life insurance can find a large number of text books 
from which to choose. For our purpose it is unnecessary 
to follow the subject further. Tables of net annual and 
single premiums will be found on pages 57 and 58. 



Note. — In whole-life insurance, as has already been shovn, the fund at 
the end of the last year (age 95, American Table) will equal the total 
amount of the insurance. In term insurance as above, the fund at 
the end of the last y- ar is not equal to the total amount of the insurance, 
but is equal to the amount of insurance which is to be paid as d a!h 
c aims during that year. 



The A B C of Life Insurance. 25 



CHAPTER IV. 

GROSS OR OFFICE PREMIUMS. 

To the net premium must be added a certain amount 
with which to pay the expenses of conducting the business 
and to provide for contingencies. This amount is called 
the margin or loading. It is usually a percentage of the 
net premium. The loading and net premium together con- 
stitute the gross or office premium — that which the com- 
pany charges for the insurance. Thus, from our example 
illustrating the computation of a net premium we have 

Net premium for a five-year term insurance of $1000, age 40 $9.86 

Margin or loading, say 33^ per cent 3.29 

Gross or office premium $13. 15 

The loading is usually a percentage of the net premium. 
Its amount varies with the form of the insurance and the 
objects which the company has in view. If it is intended 
to return a portion of the premium in the shape of divi- 
dends to the policyholder, the loading will be higher than 
when no such return is contemplated. Premiums so loaded 
are called "mutual" or "participating" premiums. Those 
from which no dividend is paid are called " stock " or " non- 
participating " premiums. 

All annual premiums are supposed to be paid at the 
beginning of the policy year. If, by consent of the com- 
pany, the premiums are paid semi-annually or quarterly, the 
unpaid installments of the annual premium are called 
"deferred" premiums. Interest is charged on them, and 



26 The A B C of Life Insurance. 

their amount is always deducted from the amount of the 
insurance in case of a claim. As has already been stated, 
premiums are computed upon the theory that the full 
annual premium is paid at the beginning of the year, and 
the premiums are smaller than they would otherwise be. 
Consequently the company is fairly entitled to retain the 
unpaid installments. 

An analysis of the first year's premium at different ages, 
showing what portion of the net premium is used for death 
claims and what for reserve, the amount of loading, and the 
gross premium made up of these three items, is given on 
page 58. 



The A B C of Life Insurance. 27 



CHAPTER V. 
RESERVES; LOANS ; REINSURANCE, 

But little need be added to what has already been said 
concerning reserves. Their nature and function have been 
fully explained. Nor is it necessary to attempt an explana- 
tion of the method of calculating them. Remembering the 
definition of a reserve, "the difference between the present 
value of the insurance and the present value of the pre- 
miums thereon/' it will be seen that compound interest is 
again an important factor. The interest received upon the 
fund representing the reserve, or upon the securities in 
which that fund is invested, may be added to the fund from 
time to time, thus lessening the amount of the principal 
which must be set aside for investment. 

To put it in another way, it is evident that if a company 
is to receive interest on its investments, it need not reserve 
so much money at the present time to meet a certain 
amount of future liabilities as it would have to reserve if no 
interest were to be received. Also, the higher the rate of 
interest the smaller the reserve required. If you must have 
$1000 at the end of a year, and can get but 4 per cent 
interest, you must put aside or reserve at the beginning of 
the year $961.54. But if you can get 10 per cent you 
need reserve only $909.09. Reserves are usually calculated 
upon the basis of the Actuaries' Table with 4 per cent 
interest, or the American Experience Table with 4 \ per 
cent interest. Of course those calculated on the latter 
basis are the smaller. The following table shows the 



28 The A B C of Life Insurance. 

reserves on a policy of $1000, issued at age 35, computed 
according to the different standards ■ 

American Experience Actuaries' 
with 4I4 per cent Interest, with 4 p^r cent Interest. 

End of 1st year $9.82 $11.48 

End cf 5th year 53- 2 ° 6134 

End of io'h year H7-45 133 41 

End of 15th year 193-43 21430 

End of 20th year 2 79-59 3 OI -35 

The percentage of difference decreases with the age of 
the policy, that is, the number of years it has been in force. 

Tables of Reserves according to the higher standard, the 
Actuaries' Table of Mortality with 4 per cent interest, are 
given on pages 54 and 55. These are the reserves on pre- 
mium-paying, ordinary life policies. The reserves on paid-up 
policies are, of course, the net single premiums given in the 
table on page 57. 

There are many-i orms of insurance, as will be seen from 
chapter VII. Each corresponding form of policy has its own 
special premium, which must, of course, provide for its own 
sufficient reserve. The net premiums and reserves given in 
the tables herewith, are those on the most ordinary form of 
life policy only. These are sufficient, in the way of 
elementary illustration, for the present purpose. 

From the nature of a reserve, it is always reckoned a 
liability of the company. It must be kept intact for its 
proper use, as already explained. If it is not, and the im- 
pairment is too great to be made good, the laws of the dif- 
ferent States require, under differing conditions, the winding 
up of the company, upon the theory that, although the 
company may be amply able to pay its current claims, the 
time will surely come when it will be unable to do so. 
Consequently the matter of suitable investments which shall 
be safe, and at the same time shall return a fair rate of in- 



The A B C of Life Insurance, 29 

terest, is one of prime importance to a company. The 
laws of most States prescribe the forms of investments which 
a company may make. 

It should be noted in passing that the larger the reserve 
on a policy, the less the amount which the company has at 
risk in the insurance. Thus, if the reserve on a policy of 
$ioco is $500, it is evident that the company need add but 
$500 from its current income to make up the full amount 
of the insurance. From this point of view, and regarding 
the reserve in the light of a deposit made by the policy- 
holder with the company, Mr. Elizur Wright gave to the re- 
serve the definition of " self-insurance." The actual loss to a 
company through death claims is not the total amount of 
those claims, but the difference between that amount and 
the total amount of the reserves credited to the policies 
under which the claims are paid. 

The following table shows the accumulation of the re- 
serve under a policy of $1000, ordinary life plan, issued at 
age 40. Column 1 gives the portion of the premium which 
is set aside each year for reserve. This diminishes each 
year, as the actual cost of insurance increases each year. 
Column 2 gives the total amount of the reserve held by 
the company at the end of each year. Of course, at the end 
of the first year, this is the reserve portion of the first year's 
premium, with one year's interest at four per cent added. At 
the beginning of the second year, the reserve portion of the 
second year's premium is added to the total amount of reserve 
held at the end of the first year. To this sum, one year's 
interest at four per cent is added, and the total is the reserve 
at the end of the second year. And so on for each year. 

The net amount at risk is obtained by subtracting the re- 
serve held by the company at the end of each year, from 
$1000, the full amount of the insurance. 



3° 



The A B C of Life Insurance, 



Accumulation of Reserve; Decrease of Amount 
at Risk. 

Amount insured, $1000. Ordinary life plan. Age at 
issue, 40. Reserve computed according to American Ex- 
perience Table, with four per cent interest. 



Year. 


Reserve Portion 
of Premium. 


Accumulated Re- 
serve at End of Yeai 


Net Amount 
at Risk. 


1st 

2d 

qd 


$13.06 
12.99 

12. 9E 
12.82 
32.70 

12.57 

I2.4O 

12.22 

I2.00 

H-73 

11-43 

II.08 

IO.7I 

IO 29 

9 83 

9-34 

8.80 

8.23 

7 65 

6.96 

etc. 


$1359 
27.65 
42.18 
57.20 
72.70 
88.68 

io5 13 
122.05 

I394I 
157-19 
175-37 
193-91 
212.80 
232.02 
251-52 
271.30 
291.31 
3ii-52 
33I-9I 
352.42 
etc. 


$986 41 

972.35 
957-82 
942.80 
927.30 


•3 , 

4th 

qth 


6th 


911.32 


7th 


894.87 


8th 


877.95 


oth 


860.59 


10th 


842.81 


nth 

12th 


824.63 
806.09 


13th 


787.20 


14th 


767.98 


15th 


748.48 


16th 


728.70 


17th 


708.69 


18th , 


688.48 


19th 


668.09 


20th 

etc. 


64758 

etc. 



Premiums are sometimes paid, by consent of the com- 
pany, partly in cash and partly in notes. These notes are 
available as a part of the reserve. The cash part of the 
premium is used to pay expenses and current losses, and 
the note is laid away as part of the reserve. Such notes 
are called " premium notes " and in reality constitute a loan 
to the policyholder. The premium note system has not 
proved a very satisfactory one. The notes accumulate and 
finally constitute a considerable lien upon the insurance, 
which is deducted from the amount of the insurance in case 



The A B C of Life Insurance. 31 

of claim. In companies whose dividends are large, the 
accumulation of these notes is diminished by applying the 
dividends towards their payment. There are very few com- 
panies at present which use the note system. 

Policies having a large reserve value are sometimes used 
as collateral for loans. Their main value for such purpose 
lies in the reserve. The insurance itself is payable only 
upon the happening of a certain contingency, i. e., the death 
of the insured, and, of course, constitutes a very indefinite 
form of security. Endowments (policies payable when the 
insured reaches a certain age, or at prior death) are more 
available as collateral security, but even here the definite 
value of the collateral is largely dependent upon the amount 
of the reserve. 

The amount of money allowed by a company for the 
surrender of a policy is governed by the reserve, unless 
the insured is in poor health. In that case the prospect of 
his early death, which would make the policy a claim for 
the full amount of the insurance, would give an added 
present value to the policy. It is evident, however, that, 
if the insured be in good health, the reserve on his policy 
represents his entire equity in the insurance, since the 
remaining portion of his premiums has been used for the 
payment of current losses and expenses. 

Usually companies do not allow the full reserve as a sur- 
render value, but deduct from it a " surrender charge," as 
it is called. This charge varies in amount. The Massa- 
chusetts non-forfeiture law allows 20 per cent. 

In cases of reinsurance, the reserve is again the important 
element of the transaction. If a company wishes or is 
forced to withdraw from business, it sometimes reinsures its 
risks, i. e., transfers them to another company. This latter 
company assumes the contracts of the former, and charges 



$2 The A B C of Life I?isurance. 

the same premium for the insurance which each policyholder 
was paying the original company. To enable it to do this, 
the reserve fund accumulated by the original company 
must be transferred to the reinsuring company, else the lat- 
ter company would be the loser by the transaction, by at 
least the deficiency of the reserve. Consequently, a com- 
pany which has impaired its reserve to any considerable 
extent cannot reinsure its risks. 

The reserve is sometimes called the "reinsurance" re- 
serve. 



The A B C of Life Insurance, 33 



CHAPTER VI. 

SURPLUS j DIVIDENDS. 

The surplus of a company is the excess of its assets over 
its liabilities. The former include such real estate as the 
company may own, cash on hand and in course of trans- 
mission, stocks, bonds, mortgage loans, loans on collaterals, 
premium notes, accrued rents and interest, and deferred 
premiums less the loading. The liabilities include the re- 
serve, unpaid death claims and all unpaid bills or current 
obligations. The reserve will be the largest item of liability 
unless the company has been doing business but a very 
short time. If it is calculated upon a 4J per cent basis 
it will be smaller than if upon a 4 per cent basis. 
Consequently, the surplus at 4J per cent will be larger than 
at 4 per cent, by exactly the difference between a 4 per 
cent and a 4^ per cent reserve. In some of the older and 
larger companies this difference amounts to several million 
dollars. 

The sources of surplus in any company are three, viz. : 
A lower rate of mortality than was assumed in the compu- 
tation of the premiums ; 

A higher rate of interest, actually received, than was 
assumed in that computation ; and 

The use of a less amount of money for expenses than was 
provided for by the loading of the premiums. 

If exactly the tabular rate of mortality were experienced, 
exactly the assumed rate of interest were realized, and ex- 



34 The A B C of Life Insurance, 

actly the amount of the loading were used for expenses, the 
company would at all times have its reserve on hand, but 
not a dollar of surplus. (Surplus and reserve should be 
carefully distinguished. They are entirely separate and dis- 
tinct. One is an asset, the other a liability. One can be 
used for such purposes as the company thinks best. The 
other can be used only in the payment of claims under 
policies which have contributed to it, and in exact propor- 
tion to the amount of such contribution.) 

The rate of mortality in any well-managed company 
should be less than the assumed or tabular rate. 

The rate of interest has for many years averaged more 
than 4 per cent. For at least ten years subsequently to 
1865 it averaged 8 per cent. Its constant tendency, how- 
ever, is to become lower. Consequently, one exceedingly 
important factor in producing surplus in earlier years has 
grown less and less important in later years. 

The amount used for expenses ought not to equal the 
loading in any company which has a considerable amount 
of business, especially if the premiums are heavily loaded. 

After retaining a surplus sufficiently large to provide for 
contingencies, it is customary among companies which issue 
policies on the mutual or participating plan to divide the 
remainder of the surplus among such of its policyholders as 
are entitled to share in it. This is, in reality, the return of 

Note. — Formerly, if a p©licy "lapsed" — became void for non-pay- 
ment of premium when due — the entire accumulated reserve was forfeited 
to the company, and from this source no inconsiderable additions were 
made to the surplus. Now, however, a more equitable practice prevails, 
and the additions to the surplus from forfeiture of reserves on lapsed poli- 
cies are at present less than formerly. In general, the most consider- 
able gain to surplus from lapsed policies, at present, arises from for- 
feitures of contingent dividends under the M Tontine " system as explained 
on page 39. 



The A B C of Life Insurance. 35 

an overcharge, but it is customary to call it the payment of 
a dividend. 

The principal plans upon which dividends are distributed 
are the percentage plan and the contribution plan. The 
former allows dividends as a percentage, either on the 
amount of the insurance or on the sum of all premiums 
paid. The latter takes account of the sources of surplus 
and of the amount which each individual policy has contrib- 
uted. For example : if the mortality has been but 80 per cent 
of the tabular rate, 20 per cent of the cost of the insurance 
under A's policy is credited to him ; if interest has been 6 per 
cent, instead of 4 per cent, 2 per cent upon the reserve 
under his policy is also credited A ; if the expenses have 
been 90 per cent of the loading, 10 per cent of the loading 
of A's premium is also credited him. The sum of these 
three items is the amount of the dividend received by A. 
This plan, now almost universally adopted, was devised by 
Mr. Sheppard Homans, assisted by Mr. D. P. Fackler. 

Dividends are paid sometimes in cash, sometimes in 
reduction of the next year's premium, sometimes by the 
addition of a certain amount of insurance to the original 
amount of the policy. In the latter case they are known as 
"reversionary" dividends. 

The frequency with which the accumulated surplus is 
divided, and, consequently, the periods at which dividends 
are declared, vary with different forms of policies and the 
practice of different companies. Sometimes dividends are 
paid annually. In other instances, as under policies written 
upon the twenty-year distribution plan, they are paid once 
in twenty years, and only upon such policies as are then in 
force. 



36 The A B C of Life Insurance. 



CHAPTER VII. 

PLANS OF INSURANCE. 

The words " insurance " and " policy " are often used 
interchangeably, thus : " An insurance of five thousand 
dollars/' or " A policy of five thousand dollars." 

Life Policies. 

A policy payable only upon the death of the insured is 
known as a life policy. When the premiums are paid an- 
nually (or in semi-annual or quarterly installments) during 
the lifetime of the insured, the policy is called an ordinan', 
whole-life policy. 

When the payments are to be completed in a given num- 
ber of years, the term limited-payment life policy is used. 
Or, the exact term is mentioned as " ten-payment life," 
''fifteen-payment life," etc. The payment of a single pre- 
mium constitutes a single-payment life policy. Of course, 
all limited-payment premiums are higher than ordinary pre- 
miums, since the equivalent of payments during a lifetime 
must be contained in the limited number of payments made. 
Consequently, the reserve or self-insurance element is also 
larger. Joint-life policies are contingent upon two lives, 
both of which are insured under one policy, the insurance 
being payable to the survivor upon the death of either. 
The premium is higher than that upon a single life, but is 
not equal to the sum of the full premiums on both lives. 
Policies of this form are not in favor with American com- 
panies at the present time, 



The A B C of Life Insurance, 37 

Very intricate calculations are involved in the computa- 
tion of joint-life premium rates. 

Term insurance is insurance covering a specified term. 
This provides for payment on account of such deaths only 
as occur during the term. The example on page 23 is an 
illustration of a five-year, term insurance. As will be seen 
by examination, out of 78,106 persons living at age 40, 
only 3933 will die during the succeeding five years. If the 
term of the insurance, then, is limited to five years, the pre- 
mium need be only large enough to provide for 3933 deaths, 
while a whole-life insurance would require provision for 
78,106 deaths. The term premium is consequently lower. 
When the policy provides for insurance for a specified term, 
with the privilege of renewing the insurance at the end of 
that term for another similar term, upon payment of a pre- 
mium adjusted to the cost of each successive term, it is 
called a renewable term policy. The length of the term is 
indicated by such nomenclature as " yearly renewable term," 
or " ten-year renewable term." 

Annuities. 
These policies provide for the payment of a certain 
yearly sum to the insured, or to the beneficiary named in 
the policy, during the life-time of the annuitant. The 
premium may be paid in one payment, or in annual pay- 
ments for a given number of years. Its amount depends 
upon the relative ages of the insured and the annuitant. 
Thus if A, being 25 years old, insures his life for the bene- 
fit of his mother, 60 years old, with the understanding that 
the insurance is to be an annuity, payable, in the event of 
his death, during the remainder of his mother's life, the 
premium would be very small. For the probability is that 
A will survive his mother — in which case the company 



38 The A B C of Life Insurance, 

would have to pay nothing — or, in any event, that he will 
pay a considerable number of premiums to the company, 
while his mother will not live many years after his death 
to receive her annuity. On the contrary, if B, the insured, 
were an old man, and his daughter, the beneficiary, were 
young, the chance would be that B would pay comparatively 
few premiums, while the daughter would survive him many 
years to receive her annual stipend. In such a case, the 
premium would be very high. Annuities, while quite pop- 
ular in Europe, are little sought after in this country. 

Endowments. 

An endowment, pure and simple, is an agreement to pay 
a certain sum of money when the insured shall have 
reached a certain age. This form unmodified is almost never 
used, but there is added to it an agreement to pay the sum 
insured if the person insured shall die before reaching the 
specified age. Thus, an endowment assurance of $1000 at 
60 means that the company will pay $1000 if the insured 
reaches the age of 60, or upon his death at any time before 
that. The premium therefore must be the sum of two 
premiums, one covering the insurance for the term, and 
the other providing for the endowment at the end of the 
term. 

Endowments are sometimes classified by the age which 
the insured must attain in order to receive the amount of 
the policy ; thus, an " endowment at 60," an " endowment 
at 70." They are more commonly classified by the term 
covered. Thus, an endowment on a life, age 40, payable 
at a g e 55? would be called a " 15-year endowment." If 
a premium was to be paid each year during this term, the 
policy would be called an "ordinary 15-year endowment." 
If, however, the premiums were to be paid in 10 years, the 



The A B C of Life Insurance. 39 

policy would be called a " ten-payment, 15-year endow- 
ment." 

The rate of premium is, of couise, determined by the 
length of the endowment term and the number of payments. 

Return Premium Policies, Six Per Cent Bond 
Policies, Etc. 

Some forms of policies stipulate that upon the death of 
the insured the amount of the premiums paid by him shall 
be returned in addition to the amount named in the policy. 
Other policies guarantee the payment of the amount of the 
insurance with 6 per cent interest thereon. Of course, in 
either case and in all similar cases, the addition to the 
amount named in the policy is just so much additional 
insurance, and an additional premium must be, and always 
is, charged therefor. 

Tontines. 

In 1648, Lorenzi Tonti organized a fund in Naples, the 
conditions of which were as follows : Each subscriber paid 
a certain sum of money into the fund. The total fund was 
invested, and the interest on the amount of each subscrip- 
tion was paid, during the lifetime of the subscriber, to 
such person as he named. At the death of a subscriber his 
subscription was forfeited to the fund, and the interest 
thereon was divided among the subscribers, who, for this 
purpose, were divided into classes according to age. At 
the death of the last subscriber the entire capital subscribed 
reverted to the crown. 

It will be seen that this is the opposite of life insurance, 
since those who live longest receive the greatest benefits. 
The principle of forfeiture on the part of those who die and 

NOTE.— An ordinary life policy is practically an endowment at age 96. 



40 The A B C of Life Insurance. 

of accumulation for those who survive, is known as the 
"Tontine ,, principle. This was first applied to life insur- 
ance as follows : 

It is evident that a policyholder who has paid premiums 
for several years and then given up his insurance, paying no 
further premiums, leaves in the hands of the company the 
reserve credited to his policy, and also any share in the 
surplus which might fairly be considered his, but which has 
not been actually paid to him in the form of dividends. The 
entire amount of this reserve and of this surplus was credited 
by the company to the other policies of the same form and 
class. If any policy became a death claim the face of the 
policy only was paid, and any accrued but undivided sur- 
plus thereunder was credited in like manner. Finally, at 
the end of a specified number of years, known as the Tontine 
period, the gains from these sources were divided among the 
holders of such policies, of this form and class, as then re- 
mained in force. This practice has been modified so that 
in most cases the Tontine principle is now applied to surplus 
only, the retiring policyholder receiving an equitable con- 
sideration in paid-up insurance (see page 42) for his reserve. 
Of course, with the same amount of lapses, the returns to 
persistent policyholders under present Tontine policies are 
not, and cannot be, so large as they were when the retiring 
policyholder forfeited his entire reserve as well as his ac- 
crued and unpaid surplus. The Tontine principle is appli- 
cable to any form of policy written upon mutual or partici-. 
pating premiums. The methods of application are quite 
numerous, and the policies are variously designated as, Semi- 
Tontine, Free Tontine, Five, Ten, Fifteen or Twenty-year 
Distribution policies, etc. The extent to which the principle 
is applied and the amount of the return which may reasonably 
be expected therefrom, can be determined only from a knowl- 
edge of the terms and conditions of the policy in each case. 



The A B C of Life Insurance. 41 



CHAPTER VIII. 

LAPSED POLICIES AND PAID-UP 
INSURANCE. 

If a policy ceases to be in force solely because a stipu- 
lated premium is not paid, it is said to lapse. The question 
arises, what ought to be done with the reserve credited to 
that policy, which is practically a deposit made with the 
company by the policyholder in excess of the actual cost of 
the insurance to date. In the earlier history of life insur- 
ance, the entire reserve was forfeited to the company in case 
of lapse. At the present time, the fairer practice of recog- 
nizing the policyholders' equity in this fund is universal. 
Under the old practice, if the reserve on a policy was more 
than equal to the present value of the profit which the com- 
pany might hope to make out of the future premiums on 
the policy, the lapse of that policy was a source of profit to 
the company. Now, however, the profit arising from lapses 
is almost nothing, and the lapse of a policy on any but a 
seriously impaired life is simply a matter of loss to the com- 
pany. 

In deciding what to do with the reserve on a lapsed 
policy, two things must be borne in mind: 

First. The man who is in sound health will be likelier to 
let his policy lapse than the man who has reason to fear 
that his health is impaired and his chance of life shortened. 
Consequently, in this respect, the "selection," as it is 
termed, will always be against the company. As a matter 



42 ■ The A B C of Life Insurance. 

of self-protection, and, in fact, of equity between the retiring 
policyholder and those who remain, it is but right that the 
company should retain a reasonable portion of the reserve. 
The amount so retained is called a " surrender charge."* 

Second. It may not always be convenient for a company 
to return the reserve in cash. It is necessary that the com- 
pany should obtain a certain rate of interest on its invest- 
ments, and it cannot afford to keep on hand too large an 
amount of uninvested money. Investments must also be 
made in the best class of securities and in those having a 
long time to run. Consequently, no reasonable man can 
expect an insurance company to hold itself in readiness to 
return in cash, and at any time, the reserves on lapsed poli- 
cies. 

Some companies do agree, however, to pay a certain por- 
tion of the reserve in cash at stated intervals. Thus, if a 
policy lapses at the end of the fifth, tenth or fifteenth year, 
the stipulated amount may be paid in cash. 

The usual method, however, is to treat the reserve, less 
the proper surrender charge, as a single premium, either to 
continue the full amount of the insurance for such a term 
as this single premium will cover, or to buy paid-up insur- 
ance of a less amount. In the former case, if the death of 
the insured occurs during the term of the "extended" in- 
surance, the full amount of the policy is paid, but when the 
term expires the insurance is ended. In the latter case, 
the reduced amount of the paid-up policy is paid whenever 
the death occurs. 

To find approximately the value of a whole-life reserve in 
paid-up whole-life insurance, take 80. per cent of the reserve 
and divide it by the single premium given in the table on 

* The Massachusetts " non-forfeiture " law allows a surrender charge 
of 20 per cent of the reserve. 



The A B C of Life Insurance. 43 

page 57, for the age attained by the policyholder at the 
time of lapse. 

To find the term of the extended insurance is not so 
easy. The Massachusetts non-forfeiture law with the tables 
published by the Massachusetts Insurance Commissioner, 
and also the tables published by several companies, are the 
best guide. 

On all limited-payment "policies it is customary to give 
paid-up insurance for as many proportionate parts of the 
original amount as there have been premiums paid. 
Thus 4 premiums paid on a ten-payment life policy of 
$1000 would secure paid-up insurance of $400 payable at 
death ; 7 premiums paid on a ten-payment endowment of 
$1000 at 60 would secure a paid-up endowment of $700 
payable at 60. 



44 The A B C of Life Insurance. 



CHAPTER IX. 

CERTAIN CONDITIONS IN POLICY 
CONTRACTS. 

Payments of Premiums. — Premiums are always payable 
at the home office of the company, but, for the convenience 
of the policyholder, are allowed to be paid at some bank or 
agency near him. Prompt payment of premiums is also re- 
quired. In actual practice, this is often waived, although 
there would seem to be no good reason why the insured 
should not pay his premiums with the same promptness 
which he expects and demands from the company in the 
payment of its losses. 

Residence and Occupation. — The conditions of policies in 
regard to these matters are usually exceedingly liberal. 
Residents in notoriously unhealthy localities, or persons en- 
gaged in extra-hazardous occupations, would not be 
insured by any company at the usual rates of premium. 
Policies provide that, after being insured at the usual rate, 
the policyholder shall not reside in such localities or engage 
in such occupations without first obtaining the company's 
consent and paying an extra premium therefore. The 
written consent of the company is called a " permit." 

Use of Stimulants and Narcotics. — Policies often provide 
that the insured shall not indulge in the use of stimulants 
or narcotics to such an extent as to impair his health or 
shorten his life. 

Suicide. — The practice of different companies differs as 
to suicide. Some policies provide that death by suicide, 
whether the insured be sane or insane, shall not constitute 



the A B C of Life Insurance. 45 

a claim against the company. In others, death by suicide 
from insanity is treated as the natural termination of the dis- 
ease. In others, no reference is made to suicide. 

Non-Forfeiture. — As already stated, nearly every com- 
pany now allows some equitable return, in the way of paid- 
up or extended insurance, for the reserve left in its hands by 
the lapse of a policy. Provision for this is made by the 
terms of the policy, and consequently this equity is not for- 
feited by failure to pay a stipulated premium. 

Licontestability. — Many policies provide that, subject to 
the conditions of the policy in regard to residence, occu- 
pation, and the payment of premiums, the insurance shall 
be incontestable after a certain number of years (two or 
three), except for fraud in obtaining the policy. Sometimes 
this last clause is omitted. The general effect of the pro- 
vision, however worded, is to waive, in case of claim against 
the company after the specified term, all defenses of a merely 
technical nature, or such as might be based upon misstate- 
ments in the application, made without fraudulent intent. 
No company can so effectually waive its right to contest a 
fraud, as to be estopped from making such defense if good 
grounds for it exist. The sensible man will undoubtedly admit 
that there is no more reason why attempted fraud upon an 
insurance company should not be resisted, than there is for 
non-resistance to any other form of fraud. Attempts of this 
sort sometimes occur, and are either fought out in the courts 
or settled by compromise as a matter of expediency. Resist- 
ance to such claims is always creditable to a company, and 
should have the support of agents and policyholders. On 
the other hand, the fact that a company frequently resists 
the payment of claims or forces compromises, may be ac- 
cepted without hesitation as proof that something is wrong 
in the management. 



46 The A B C of Life Insurance. 



CHAPTER X. 

APPLICATIONS; RISKS; MEDICAL 
EXAMINERS. 

When a person desires insurance, he makes application 
therefor upon printed forms furnished by the company. It 
is intended that this form, when properly filled out and 
accompanied by the report of the Medical Examiner, shall 
furnish the company with information which will enable it 
to decide whether or not the applicant is a desirable risk. 
His family history as to longevity, existence of hereditary 
diseases, etc. ; his own personal history as to health or 
disease, residence, occupation, etc.; his present residence 
and occupation, and, last but not least, his present physical 
condition, must all be taken into the account. 

It is here that the Medical Examiner plays a most 
important part. It is his duty to ascertain the present 
physical condition of the applicant, and from the results of 
his examination, together with the personal and family 
history of the applicant, to determine the probability of a 
long or short life, and consequently to recommend or reject 
the risk. No one performs a more important duty in 
connection with the whole business of life insurance. If 
Medical Examiners are incompetent or careless, the best 
plans of insurance and the ablest management will end in 
nothing but disaster. The fact that not one of the import- 
ant failures of life insurance companies in this country has 



The A B C of Life Insurance, 47 

been due primarily to excessive mortality, speaks volumes 
for the skill* and fidelity of the Medical Examiners. 

It might appear, at first sight, that a rigid medical exam- 
ination should result in a large saving to the companies by 
securing for them an exceedingly low rate of mortality. It 
is true that the rate is generally very low for a year or two 
among newly selected risks, but the effect of the medical 
selection disappears more rapidly than is usually supposed, 
and but a comparatively short time elapses before the aver- 
age normal rate is experienced. The very low cost of 
insurance in assessment organizations, newly organized, is 
due to the fact that the risks are newly selected, but it is 
idle to expect that the cost can be kept down to that point 
by the infusion of " new blood," or by any other process. 

If impaired or doubtful risks were not summarily rejected, 
the selection against the company, already alluded to, would 
assert itself at the very outset. The better class of lives 
would drop out, and the company would find itself over- 
whelmed by the mortality among the poorer risks remaining. 

Companies have been formed for the insurance of im- 
paired lives at an adequate rate of premium. It has been 
found very difficult, however, to determine what premiums 
are adequate, and the experiments in this direction have 
never proved successful. 



48 The A B C of Life Insurance* 



CHAPTER XI. 
ANNUAL STATEMENTS; RATIOS. 

The laws of the different States require companies to file 
annually statements of their transactions during the pre- 
ceding year, and of their financial condition at the close of 
the year. The forms prescribed by the Insurance Depart- 
ments of the various States are very complete. The results 
in detail are published in the annual reports of the Depart- 
ments, and are frequently accompanied by tables of per- 
centages and ratios. In determining the value of these, 
some knowledge of the business of life insurance, and more 
common sense, are necessary. For instance : 

Percentage of expenses to income is not always a reliable 
standard by which to judge economy of management. 
Premiums may be very heavily loaded for certain forms of 
insurance, and the current year's expenses may exhaust but 
a small part of that loading. Or the investment part of the 
premiums may be very large, and the premiums, con- 
sequently, very high. The amount used for expenses 
would, in either case, constitute but a comparatively small 
percentage of the gross premiums. On the other hand, the 
loading, or the investment part, or both, of premiums may 
be very small, in which case, although expenses may be 
kept within the loading, they may still constitute a com- 
paratively large percentage of the premiums. Consequently 



The A B C of Life Insurance, 49 

equal economy of management will not necessarily result in 
the same, or even nearly the same, percentage of expense 
to premium income. 

The ratio of assets to liabilities is of little consequence 
until both assets and liabilities have reached respectable 
proportions. If A has but one dollar in the world, and 
owes nothing, the ratio of his assets to his liabilities is 
infinity. If B, however, is worth $200,000, and owes 
$100,000, the ratio of his assets to his liabilities is only two 
to one. Of course, after a company has been in business 
for a number of years and has placed a large amount of 
insurance on its books, the percentage of its assets to its 
liabilities is a question of the highest importance. 

The percentage of death losses to the mea?i amount in- 
sured during the year affords the basis of a fairly close esti- 
mate of a company's mortality experience. But an exact 
determination of that experience cannot be made without a 
knowledge of the ages of all the persons insured, and conse- 
quently of the percentage of mortality expected by the com- 
pany and provided for in the premium charges. 

The percentage of interest {including rents and profits on 
sales of stocks ■, bonds and real estate) to mean amount of 
assets, is important. If premiums are calculated and 
reserves held upon a basis of 4 per cent, that rate, at least, 
ought actually to be realized. 

The ratio of expenses to amount of new business secured 
may be of much or little importance, depending entirely 
upon the proportion of expense fairly chargeable to the 
securing of new business, as well as upon the provision for 
that expense made in the premiums charged. 

The ratio of assets to amount of insurance in force 
is of little value, the main question always being whether 
present accumulations, together with future premiums, 



5° 



The A B C of Life Insurance, 



are sufficient to provide for future claims. If future pre- 
miums alone are sufficient, the question of present accumu- 
lation is of no consequence. 

And so on. Persons of a statistical turn of mind are 
constantly furnishing tables of ratios and percentages, com- 
parative tables, etc., etc. Most of the statistics thus compiled 
are interesting, many of them are valuable, a few are vital. 
Anyone well grounded in the elementary principles of life 
insurance, and fairly familiar with the practical workings of 
the business, can decide for himself to which class belong 
such statistics as come under his observation. 



" Expectation " Table. — Assured Lives. 

(Constructed from the American Experience Table of Mortality.) 



Age. 


Expecta- 
tion, 
Years. 


Age. 


Expecta- 
tion, 
Years. 


Age. 


Expecta- 
tion, 
Years. 


io 


48.7 
48.I 

474 
46.8 
46.2 

45-5 
44.9 
44.2 

43-5 
42.9 
42.2 

415 
40.9 
40.2 

395 
38.8 

38.1 
37-4 
3 6 7 
36.0 

35-3 
346 
33 9 
33-2 
3 2 5 
31.8 
3i-i 


07 


30-4 
29 6 
28.9 
28.2 

27-5 
26.7 
26.0 
25.3 
24-5 
23.8 
23.1 
22.4 
21.6 
20.9 
20.2 

19.5 

18.8 
18. 1 

174 
16.7 
16. 1 

154 
14.7 
14. 1 

13 5 
12.9 
12.3 


64 


II. 7 


ii 


q8 


65 


12 


39 


66 


10.5 


IQ 


40 


67 


14. 


41 


68 


9-5 
9 

8-5 
8 


ic 


42 


6q... 


16 


43 


70 


17 


44 


71 


18 


45 


72 


7.6 

7-1 
6. 7 

6-3 
5-9 
5-5 
5-i 
4.8 
4.4 
4.1 
3-7 
3-4 
3-i 
2 8 


19 


46 


70 


20 


47 


74 


21 


48 


7^. . 


22 


49 


j6 


23 


50 


jj 


24 


51 


78 


25 


52 


7Q 


26 


53 


80 


27 


54 


81 


28 


55 

56 


82 

83 

84 


2Q 


30 


57 


31 


58 


85 


02 


CQ 


86 


2 5 
2 2 


QQ 


60 


87... 


34. 


6l 


88 

8q 


1.9 

1.7 
1.4 


qc 


62 


06 


63 


QO 









The A B C of Life Insurance. 
American Experience Table of Mortality. 



5i 



u - 


bfl 


>H 




c 

3 


. 5 £ « 


c 


Q . 


bfl.5-^^ 


> bfi 


bfl rt 




•1 c 


a <u 


C/2^ c 


Hi -S 


'&* 


ft Q • S 


O.S 


Q 


aJ^J^.S 


^ ^ 


d 


$ ° <u 


PQ 


£ 


q"« 


ICO.OOO 


749 


.OO749O 


99.251 


746 


OO7516 


98-505 


743 


•O07543 


97,762 


74° 


.OO7569 


97,022 


737 


.CO7596 


96,285 


735 


.OO7634 


95.550 


732 


.OO766I 


94,818 


729 


.OO7688 


94,089 


727 


.OO7727 


93.362 


725 


.OO7765 


92,637 


723 


.OO7805 


91,914 


722 


.OO7855 


91,192 


721 


.OO7906 


90,471 


720* 


•OO7958 


89.751 


719 


.O080II 


89032 


718 


.O08065 


88314 


718 


.O0813O 


87596 


718 


.O08197 


86,878 


718 


.CO8264 


86,160 


719 


.O08345 


85.441 


720 


.0:8427 


84,721 


721 


.O085IO 


84,000 


723 


.O08607 


83,277 


726 


.008718 


82.551 


729 


.O0883I 


81,822 


732 


.OO8946 


81,090 


737 


.OO9089 


80,353 


742 


•OC9234 


79,611 


749 


.OO9408 


78,862 


756 


.CO9586 


78,106 


765 


•CO9794 


77,341 


774 


.OIOGO8 


76,567 


785 


.OIO252 


75.782 


797 


.OIO517 


74.985 


812 


.OI0829 


74.173 


828 


.OIII63 


73.345 


848 


.OII562 


72497 


870 


.012000 


71,627 


896 


.OI2509 


70.73 1 


927 


.OI3I06 


69,804 


962 


.OI3781 


68,842 


I,COI 


.OI454I 


67,841 


1,044 


.OI5389 



Age. 



53 
54 
55 
56 
57 
53 
59 
60 
61 
62 
63 
64 
65 
66 

67 
68 
69 
70 

7i 
72 

73 
74 
75 
76 
77 
73 
79 
80 
81 
82. 
83 
34 
85 
86 
87 
S3 
89. 
go 

91 

92 

93 
94 
95< 



u 


bfl 




C 




u 

3 


G O 


Q .- 


> bfl 


bfl 3 

a <u 


3.5 


'>> 


O C 


A 


&*3) 


d 


pq 


& 


66,797 


1,091 


65,706 


1. 143 


64-563 


1,199 


63.364 


1,260 


62,104 


1325 


60,779 


1.394 


59.385 


1,468 


57.917 


1.546 


56,371 


1,628 


54.743 


1,713 


53.030 


1,800 


51.230 


1,889 


49.341 


1,980 


47.36i 


2,070 


45,291 


2,158 


43- I 33 


2243 


40,890 


2.321 


38,569 


2,391 


36,178 


2,448 


33.730 


2,487 


31.243 


2,505 


28,738 


2,501 


26 237 


2,476 


23,761 


2431 


21,330 


2,369 


18,961 


2 2QI 


16,670 


2,196 


14.474 


2,091 


12,383 


1,964 


10,419 


I,8l6 


8603 


1,648 


6,955 


1,470 


5.485 


1,292 


4.193 


1,114 


3.079 


933 


2,146 


744 


1,402 


555 


847 


385 


462 


246 


216 


137 


79 


58 


21 


18 


3 


3 



<j ~5 rt 

°^ r oC>i 
<u bJG c ; 

w C £ 

SQ ..5 

u,„oa 



•016333 
.017396 
.018571 
.019885 
•021335 
.022936 
.024720 
.026693 
.028880 
.031292 

•033943 
.036873 
.040129 
.043707 
.047647 
.052002 
..056762 
.061593 
.067665 

.073733 
.080178 
.087028 
.094371 
.102311 
.111064 
.120827 

•I3 I 734 

. 144466 
.158605 
.174297 
.191561 
.2H359 
.235552 
.265681 
.303020 
.346692 
.395863 
•454545 
.532466 

•634259 

■734*77 

.857143 

1. 000000 



5* 



The A B C of Life Insurance. 



Actuaries' or Combined Experience Table 
of Mortality. 

The following table was prepared by a committee of 
eminent actuaries on the data afforded by the combined 
experience of seventeen of the principal life insurance offices 
in England. It was deduced from 62,537 assurances. Some 
of the objections advanced against it are that certain lives 
have been more than once assured, have appeared twice or 
oftener as elements of the calculation, and that the data for 
the older ages were insufficient. The average duration of all 
the policies was a little less than eight and a half years. The 
later Actuaries' or H. M. (healthy males) Table is now more 
generally used in England. The American Experience Table 
furnishes a better standard than either for American lives : 



Age. 


ih 

.- c v 
E <u 


u * J 

Is 

3 


Percentage of Deaths 

During the Year to 
Number Living at the 
Beginning of the Year. 


Age. 


■5 J 

bX)43 

S * J 
>o 
iJ bJO 

M.S 

el 


1 
■£* 

1-3 


Percentage of Deaths 

During the Year to 

Number Living at the 

Beginning of the Year. 


10 

IT 

12 

13 

14 

15 

16 

17 

18 

19 

20 

21 

22 

23 

24 


100,000 

99.324 
98,650 

97.978 

97.307 

96,636 
95.965 
95.293 
94,620 

93-945 

93,268 
92,588 

9L905 
91,219 
90,529 


676 

674 
672 
67I 
67I 

67I 
672 
673 
675 
677 

680 
683 

686 
690 
694 


.006760 
.006786 
.006812 
.006848 
.006896 

.006944 
.007003 
.007062 
.007134 
.007206 

.007291 
.007377 
.007464 
.007564 
.007666 


25 

26 

27 

28 

2 9 

30 

3i 

32 

33 

34 

35 

36 

37 

38 

39 


89.835 
89.137 
88,434 
87,726 
87,012 

86,292 

85.565 
84,831 
84.089 
83.339 

82,581 
81,814 
81,038 
80,253 
79.458 


698 

703 
708 

714 

720 

727 

734 
742 

750 

758 

767 
776 
785 
795 
805 


.007770 
.007887 
.008006 
.008139 
.008275 

.008425 
.008578 
.008747 
.008919 
.009095 

.009288 
.009485 
.009687 
.009906 
.010131 



The A B C of Life Insurance, 



53 



Actuaries' or Combined Experience Table 
of Mortality. 

{Continued from preceding page?) 



Age. 



c k* . 
.5 c u 

^ £>* 
j- wT, 

3 ,B 



78,653 
77.838 
77,OI2 

76,173 
75.3I 6 

74435 
73.526 
72,582 
71,601 
70,580 

69.517 
68,409 

67.253 
66,046 

64,785 

63,469 
62,094 
60,658 
59.I6I 
57,600 

55,973 
54,275 
52,505 
50,66l 

48,744 

46,754 
44,693 
42,565 

4°,374 
38,128 



Aw 

s 

11 



815 

826 

839 

857 



909 

944 

981 

1,021 

1,063 

1,108 
1,156 
1,207 
1,261 
i,3 l6 

i,37S 
1,436 
i,497 
1,561 
1,627 

1,698 
1,770 
1,844 
1. 917 
1,990 

2,061 
2,128 
2,191 
2,246 
2,291 



v — \Z ^ 



.OIO362 
.OI06I2 
.OIO894 
.OII25I 
.OII697 

.OI22I2 
.OI2839 

.OI35I7 
.OI426O 
.01506I 

.OI5939 
.OI6898 
.OI7947 
.OI9O93 
.O203I3 

.02l664 
.023126 
.O24679 
.O26386 
.028247 

.O3O336 
.0326I2 
.035120 
.O3784O 
.O4O826 

.O44082 
.O476I4 
.051474 
.055630 
.O6OO87 



Age. 



70 
71 

72 

73 
74 

75 
76 
77 
78, 
79 

80 
81 
82 
83 

84 

85 
86 

87 
88 

89 

90 
9:. 

92 
93 
94 

95 

t 

98 
99 



u 




,B re 


u 


-* V 


3 


*> 


«,: 


&3 






•>> 


'?*£ 


.£ 

U c 




6.S 


B 


Zpq 


fc 


35.837 


2.327 


33,5io 


2,351 


3LI59 


2,362 


28,797 


2,358 


26,439 


2,339 


24,100 


2,303 


21,797 


2,249 


19,548 


2,179 


17,369 


2,092 


15,277 


1,987 


13.290 


1,866 


11,424 


1-730 


9,^94 


1,582 


8,112 


1,427 


6,685 


1,268 


5,417 


1,111 


4,306 


958 


3,348 


811 


2,537 


673 


1,864 


545 


I.3I9 


427 


892 


322 


570 


231 


339 


155 


184 


95 


89 


52 


37 


24 


13 


• 9 


4 


3 


1 


1 



t/i V u 

,b o^b re 

•W -M -M <u 



b c_g'S 

o 5 g.s 

* Jr 5 & 



*°# 



•064933 
.070158 
.075805 
.081884 
.088468 

.095560 
.103179 
.111469 
.120444 
.130065 

. 140406 
•I5I436 
.163194 
.175912 # 
.189678 

.205095 
.222480 
.242234 
.265274 
.292382 

.323730 
.360987 
.405263 
.457227 
.516304 

.584270 
.648640 
.692308 
.750000 
1. 000000 



54 



The A B C of Life Insurance. 



Ordinary, Continued-Payment, Whole-Life. 

net value, or reserve of a premium-paying policy of 

$iooo, at the end of various years, actuaries' 

table, 4 per cent 



Age at 
Issue. 



1st 
Year. 



% 

7.60 
7.91 
8.24 
8.58 
8-93 

9-31 

9.70 

10.11 

10.54 

11.00 

11 48 

11.99 

12.55 
13.12 

13-74 

14.41 

15.12 
15-85 
1659 
17.30 

18.01 

18.69 

19-39 
20.10 
20.86 

21.62 
22.39 
23.19 
24.00 
24.85 

25.72 
26.61 
27.56 
28.52 
29.50 
3°-45 



2d 

Year. 



15-45 
16.09 

1675 
17-43 
18.16 

18.91 
19.70 
20.54 
21.42 
22.35 

23.33 
24.39 
25-51 
26.69 
27.96 

29.31 

3°-73 
32.18 

33-59 
34-99 

3 6 -36 
37-71 
39.10 

40.54 
42.02 

43-52 
45.06 
46.63 
48.26 
49-94 

51.65 
53-43 
55-29 
57-i8 
59-Q5 
60.90 



sd 


4th 


5th 


6th 


7th 


Year. 


Year. 


Year. 


Year. 


Year. 


$ 


$ 


$ 


$ 


$ 


23-56 


31.94 


40.58 


49-51 


58.73 


24.52 


33-24 


42.24 


51-52 


61. II 


25-53 


34.60 


43 96 


53-62 


63 59 


26.58 


36.02 


45-76 


55 8i 


66 20 


27.68 


37-50 


47.64 


58.12 


68.93 


28.83 


3906 


49.63 


60.54 


71.80 


30.03 


40.70 


5I7I 


63.08 


74.84 


31-31 


42.43 


53-91 


65.78 


78.04 


32.65 


44-25 


56.25 


68.63 


8i.43 


34-07 


46.20 


58.71 


71.65 


85-03 


35-59 


48.2*5 


61.34 


74.86 


88.84 


37.19 


5o.43 


64.II 


78.26 


92.87 


38.90 


52.75 


67.08 


81.87 


97.09 


40.72 


55-22 


70.20 


85.62 


101.43 


42.65 


57.83 


73-46 


89.48 


105.88 


44.70 


60.55 


76.79 


93-42 


110.36 


46.81 


63.29 


80.16 


97-35 


114.85 


48.91 


66.04 


83-49 


101.26 


119.32 


51.00 


68.73 


86.78 


105.13 


123.80 


53.02 


71.38 


90.04 


109.02 


128.28 


55.04 


74.03 


93-34 


112.94 


132.80 


57.05 


76.72 


96.67 


116.90 


137.38 


59-14 


79-47 


100.09 


120.95 


142.05 


61.28 


82.30 


103.57 


125.09 


146.83 


6347 


85-I9 


107.14 


129.34 


151-73 


65.70 


88.13 


110.79 


I33-67 


15672 


67.98 


91 14 


"4-53 


138.09 


161.84 


70.33 


94.24 


118.34 


142.64 


167.09 


72.74 


97.42 


122 29 


147-32 


172.47 


75.22 


100.70 


12635 


152.12 


177-93 


77.78 


104 08 


130.51 


156.98 


183.46 


80.42 


107.55 


134-72 


161.90 


189.01 


8315 


in. 07 


138.99 


166.84 


194-59 


85.88 


114 59 


14323 


171.76 


200.14 


88.60 


118 08 


14746 


176.66 


205.63 


91.28 


121.54 


151.63 


181.49 


211.02 



See Explanatory Notes on Page 59. 



The A B C of Life Insurance. 
Ordinary, Continued-Payment, Whole-Life. 



55 



NET VALUE, OR RESERVE OF A PREMIUM-PAYING POLICY OF 

$IOOO, AT THE END OF VARIOUS YEARS, ACTUARIES' 

TABLE, 4 PER CENT. 

( Continued from preceding page. ) 



Age at 

Issue. 



gth 


10th 


15th 


20th 


25th 


30th 


35th 


Year. 


Year. 


Year. 


Year. 


Year. 


Year. 


Year. 


$ 


$ 


$ 


$ 


$ 


$ 


$ 


78.06 


88.20 


144.12 


209.84 


283 60 


362.97 


446. IT 


81.22 


91.76 


149.99 


218.13 


293.72 


374.60 


458.86 


84 52 


95-50 


156.17 


226.62 


304-03 


386.39 


47I.67 


87.99 


99-43 


162.65 


235-3I 


3I4-5I 


398.34 


484 52 


91.64 


103.56 


169.41 


244.20 


325.18 


410.44 


497.38 


9548 


107.91 


176.42 


253-29 


336.02 


422 68 


5I0.2I 


99-53 


1 12.51 


183.65 


262.57 


347.02 


434-99 


52301 


103.82 


H7-37 


191.06 


272.02 


358.17 


447.38 


535-72 


108.36 


122.50 


198.65 


281.64 


36949 


459.80 


548.34 


II3-I5 


127.86 


206.39 


291.42 


380.94 


472.23 


560.83 


118. 16 


133-41 


214.30 


301.35 


392.53 


484.64 


573 20 


12335 


I39-I3 


222.36 


311.42 


404.18 


497.00 


58542 


128.69 


144.97 


230.54 


321.60 


4I5-89 


50927 


597-47 


134.10 


150.89 


238.83 


331-91 


427.60 


521.42 


609.34 


139.60 


156.89 


247.22 


342.33 


439-31 


533 44 


621 01 


145-14 


162.97 


255-70 


35284 


450.97 


545-32 


63247 


i5o-73 


169.09 


264.25 


363-37 


462.54 


557 02 


644.11 


156.33 


175-22 


272.83 


373-90 


473-98 


568.53 


654-7I 


161.94 


181.37 


281.47 


384 39 


485.29 


579-85 


665 47 


167.56 


187.54 


290.19 


394.86 


496.45 


590 97 


675 99 


17324 


193-79 


299.01 


405-30 


507-49 


601 90 


686.30 


179.12 


200.13 


307.89 


4I5-7I 


518.41 


612.65 


696.43 


184.90 


206.59 


316.86 


426.07 


529-23 


623.26 


706.46 


190.90 


213.19 


325.89 


436.37 


539-92 


633.69 


716.50 


197.06 


219-95 


334 98 


446.62 


55049 


64393 


726.61 


203.34 


226.84 


344-07 


456.79 


560.91 


654.00 


736.93 


209.76 


233.82 


353-18 


466.88 


571.20. 


603.94 


747.48 


216.27 


240.88 


362.24 


476.87 


581.36 


673.82 


758.32 


222.86 


248.00 


371.25 


486 76 


59I-36 


68374 


769.48 


229.51 


255.18 


380.21 


496.55 


601.20 


693.81 


780.92 


236. 19 


262.35 


389.11 


506.21 


610.89 


70415 


792.51 


242.87 


269.52 


397.92 


515-79 


620.47 


71483 


804 24 


249.54 


276.63 


406.65 


525.16 


630.03 


72588 


815.99 


256.13 


283.65 


415.26 


534-43 


639.68 


737-37 


827.41 


262.63 


290.58 


423-74 


543.52 


649.52 


749.24 


838.15 


269.02 


29742 


432.09 


55249 


659.75 


761.42 


847.87 



40th 
Year. 

530.09 

543-16 
556.13 
569.00 

581.75 

594-38 
606.86 
619.17 

63I-3 1 
643.26 

655-OI* 
666.54 
677.87 
688.96 
699.79 

710.39 
720 76 

730.97 
741-10 
751.23 

76148 
771.90 
782.51 

793 36 
804.39 

815.50 
826.66 
837.76 
848.52 
858.60 

867.73 
874.74 
879 66 
887.71 
906.81 
1,000.00 



See Explanatory Notes on Page 59. 



56 



The A B C of Life Insurance. 



Present Value of $i Due at End of Year in from 
One to Forty Years from the Present Time. 



No. of Years. 



i, 

2, 

3' 
4 
5> 
6 

7 

8. 

9 

io, 

ii. 

12. 

13' 
14. 

15. 
16. 

17. 
l8, 
19, 
20, 

21. 
22, 
23, 
24. 

25 
26, 
27. 
28. 
29. 
30 

31 
32 

33 
34 
35 
36 
37 
38 
39 
40 



Four Per 
Cent. 



961538 
924556 



854804 
821927 
79°3 X 5 
759918 
730690 
702587 
675564 

649581 
624597 
600574 
577475 
555265 
5339o8 

513373 
493628 
474642 
456387 

438834 
421955 
405726 
390121 

375 1 17 
360689 

346817 
333477 
320651 
308319 

296460 
285058 
274094 
263552 

253415 
243669 
234297 
225285 
216621 
208289 



Four and 
One-Half 
Per Cent. 



956938 
91573° 
876297 
838561 
802451 
767896 
734828 

703185 
672904 
643928 

616199 
589664 
564272 

539973 
516720 
494469 
473176 
452800 
433302 
414643 

396787 
379701 
363350 
347703 
332731 
318402 
304691 
291571 
279015 
267000 

255502 
244500 

233971 
223896 

214254 
164525 
196199 
877501 
179665 
171929 



Five Per 
Cent. 



952381 
907029 
863838 
822702 
783526 
746215 
710681 
676839 
644609 
613913 

584679 
556837 
530321 
505068 
481017 
458II2 
436297 
4I552I 

395734 
376889 

358942 
341850 
325571 
310068 

295303 
281241 
267848 

255094 
242946 

231377 

220359 
209866 
199873 

190355 
181290 
135282 
164436 
156605 
149148 
142046 



Six Per 
Cent. 



943396 
889996 
839618 
792094 
747258 
704961 

665057 
627412 
591898 
558395 

526788 

496969 
468839 

442301 
417265 
393646 
371364 
350344 
330513 
3H805 

294155 
277505 
261797 

246979 
232999 
219810 
207368 
195630 
184557 
174110 

164255 

154957 
146186 
137912 
130105 
122741 

I 15793 
109239 
103056 
097222 



The A B C of Life Insurance. 



57 



Net Premiums for a Whole-Life Insurance of $1000. 

(Based upon the American Experience Table of Mortality with 4 per 
cent interest.) 



Age. 



15 
16 

17 
18 

19 
20 
21 
22 

23 
24 

25 
26 

27 
28 

29 
30 
3 1 
32 
33 
34 

36 
37 
38 
39 
40, 
41 
42 
43 
44 

46. 

47 
48. 
49. 
5o • 
51 
52. 
53 
54- 
55- 
56- 
57 
58. 
59- 
60. 



Single Pre- 
miums which 
are also Net 

Reserves 
on Paid-up 

Policies. 



$229.68 
233.01 
236.48 
240 10 
243 86 
24777 
251-85 
256.08 
260.47 
265.04 
269.79 

274-74 
27987 
285.21 
290.75 
296 51 
30250 
308.71 

3 x 5-i7 
321 86 
328.81 
33602 
348-50 
35 J -24 
359-27 
367.57 
376 17 

38506 
394 25 
4°3-75 
4I3-55 
423.66 
434.06 
444.76 

455-74 
466.99 

478.48 
490.21 
502.15 

5I4-3I 

52665 

539-15 
55i 81 
564-59 
577.48 
590.46 



Annual Pre- 
miums 
during Life. 



$11.47 
11.68 
11. 91 
12.15 
12.40 
12.67 
12.95 
1324 
1354 
I3-87 
14.21 

14-57 
1495 
15 35 
15 77 
16.21 
16.68 
17.18 
17.70 
18.25 
18.84 
19.46 
20.12 
20.82 
21.57 
2235 
23.19 
24 08 

25.03 
26 04 
27.12 
28 27 
29.50 
3081 
32.21 
33-70 
35-29 
3698 
38.79 
4o.73 
42.79 
45.00 

47-35 
49.87 

52.57 
5545 



Annual Pre- 
miums for 
Twenty Years. 



$17-32 
I7-58 
17-85 
18.13 
18.42 

18.73 
19-05 
I9-38 
19.72 
20 08 
20.46 
20.85 
21.26 
21.68 
22.13 
22.59 
2308 

23-59 
24 12 
24.67 
25.26 

25-87 
26.51 
27.18 
27.88 
28.68 
29.41 
30.24 
31. 11 
32.03 
33-oo 
34-04 
35-14 
36.30 
37-55 
38.86 
40.27 
41.76 
43-36 
45.06 
46.88 
48.84 
5o.93 
53-17 
55-59 
58.18 



Annual 

Premiums 

for Ten 

Years. 



$28 12 

28.53 
28.96 
29.41 
29.87 
30-36 
30.87 
31-39 
31-94 
32.51 
33.IO 
33-72 
34.36 
35-03 
35-72 
36 45 
37.20 

37-98 
38.80 
39-64 
40.53 
41-45 
42 40 

4340 
44-44 
45-51 
46.64 

47-81 
49-°3 
5030 
51-63 
53- or 
54-46 
55-97 
57-54 
59 19 
60.90 
62.69 

64-55 
66.49 
68 52 
7065 
72.87 
75.20 
77.64 
80.22 



See Explanatory Notes on Page 59. 



58 



The A B C of Life Insurance. 



Annual Premiums— Analysis of First Year's Premium, at 

Different Ages, $1000 Whole-Life Insurance. 

Participating Rate. 



AGE. 



25 
26 
27 
28 
29 
30 
31 
32 
33 
34 
35 
36 
37 
38 
39 
40 

4i 
42 
43 
44 

45 
46 
47 
48 

49 
5o 
5i 
52 
53 
54 
55 
56 
57 
58 
59 
60 



Net Premiums, American Ex- 
perience Table of Mortality, 
with 4 Per Cent Interest. 



Portion 
for Deai-h 
Claims. 



$7.71 
7.76 
7.82 
7.88 
7.96 
803 
8.11 
8.20 
8.30 
8.40 

8.51 
8.64 

8.77 
8-93 
9 10 
9.29 
9.49 
9.71 

9-95 
10.24 

10.55 
10 92 
11.32 

11.79 
12.34 
12.97 
13.67 
14-45 
15.33 
16 30 

17-38 
18.60 

19-93 
21.40 
23.10 
24-85 



Portion 

for 
Reserve. 



$6.50 
6.81 
7.13 
7-47 
7.81 
8.18 

8-57 
8.98 
9.40 
986 

10.33 
10.82 

n-35 
11.89 
12.47 
13 06 
13.70 

14-37 
15.08 
15.80 
16.57 
17-35 
18.18 
19.02 
1987 
20.73 
21.62 

22.53 
23.46 

24-43 
25.41 
26.40 
27.42 
28.67 

29-53 
30.60 



Total 

Net 

Premiums 



$14.21 
14-57 
14-95 
15-35 
15-77 
16.21 
16.68 
17 18 
17.70 
18.25 
18.84 
19.46 
20.12 
20.82 
21-57 
22-35 
23.19 
24 08 
2503 
26.04 
27.12 
28.27 
29.50 
30.81 
32.21 
33-70 
35-29 
36.98 

38 79 
4o.73 
42.79 
45.00 

47-35 
49.87 

52.57 
55-45 



Loading. 



$5.68 
5 83 
5-98 
6.13 
6.30 
649 
6.67 
6.87 
7.08 
7-30 
7-54 
7 79 
8.05 

8-33 
8.62 

8.95 

9.08 

9.64 

10.02 

10.42 

10.85 

IT. 31 
II.80 
I2.32 

12 88 

13 48 

14 11 
14.80 
15-52 
16.29 
17 12 
18.00 
18.94 

19 95 
21.03 
22.18 



Gross or 

Office 

Premiums. 



$19.89 
20.40 
20.93 
21.48 
22.07 
22 70 
2355 
24 05 
2478 
25-56 
26.38 

27-25 
28.17 

29-I5 
3O.I9 

3I-30 
32 47 

33-72 
35-o5 
36.46 

37-97 
39-58 
41.30 

43 13 
45-09 
47.18 
49.40 
5I-78 

54-31 
57.02 

59 91 
63 00 
66.29 
69.82 
73.60 
77-63 



See Explanatory Notes on Page 59. 



The A B C of Life Insurance. 59 



EXP LAN A TOR Y NO TES. 



Pages 54 and 55. — Reserves are calculated upon the basis of net pre- 
miums. The amount of loading, added to the net premium to make the 
gross premium, does not affect the reserve. Upon the same kind of a 
policy, issued at the same age and with the same number of premiums 
paid, the reserve would be the same, no matter what amount of annual 
premium might be charged for the insurance. 

Under premium-paying policies, the amount of the reserve depends 
upon the age of the insured at the time the policy was issued, and 
the number of premiums paid. Under paid-up insurance, the amount of 
the reserve depends entirely upon the age of the insured at the date 
for which the reserve is computed. 

The reserves given are based upon the Actuaries' Table of Mortality, 
with 4 per cent interest. See pages 27 and 28. For the sake of exactness 
it should be said that, while these reserves are for the most part greater 
than those based upon the American Experience Table, with 4K per cent 
interest, the latter are the greater at the very highest ages. The reason 
for this is that according to the American Table the term of life ends with 
age 95, while according to the Actuaries' it continues to age 100. 



Page 57. — The net single premiums given are also the net values 
or reserves of a paid-up policy of $1000 at the different ages. To esti- 
mate pretty nearly the amount of paid-up insurance which a company 
would allow for the surrender of an ordinary whole life policy with pre- 
miums payable annually, ascertain the reserve on that policy according to 
the table of reserves on pages 54 and 55, and divide 80 per cent of it by 
the single premium given for the age actually attained by the policyholder 
at the time of surrendering his original policy for paid-up insurance. 



PAGE 58. — This table shows the component parts of b®th the net and the 
gross (or office) premiums at different ages, for an insurance of $1000, 
payable at death. This analysis, however, is correct for the first year of 
the insurance at each age only. Each subsequent year the portion of the 
premium used for death claims is greater, and the portion used for reserve 
is smaller than these respective portions for the first year. The accumu- 
lated reserve increases each year by the addition of that year's reserve 
portion of the premium and of interest, as is shown in table on page 30. 
The " loading" remains the same theoretically for each year of the insur- 
ance, although the amount actually collected by the company will vary 
with the amount of dividend allowed on that aceount. 



\r 



Library of Congress 
Branch Bindery, 1903 



illii 




